Question: Add the following rational expressions. $\dfrac{3x-10}{9x^2+18x+9}+\dfrac{-6x+3}{9x^2+18x+9}=$
Solution: We want to add two rational expressions whose denominators are equal. We can do this by adding the numerators and keeping the denominator the same. [Does this fit with how we add rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{3x-10}{9x^2+18x+9}+\dfrac{-6x+3}{9x^2+18x+9} \\\\ &=\dfrac{(3x-10)+(-6x+3)}{9x^2+18x+9} \\\\ &=\dfrac{3x-10-6x+3}{9x^2+18x+9} \\\\ &=\dfrac{-3x-7}{9x^2+18x+9} \end{aligned}$ In conclusion, $\dfrac{3x-10}{9x^2+18x+9}+\dfrac{-6x+3}{9x^2+18x+9}=\dfrac{-3x-7}{9x^2+18x+9}$